SBBTS: A Unified Schr\"odinger-Bass Framework for Synthetic Financial Time Series

TL;DR

SBBTS introduces a unified diffusion framework that jointly models drift and volatility in financial time series, improving synthetic data quality and forecasting performance.

Contribution

The paper proposes the Schr"odinger-Bass Bridge for Time Series (SBBTS), extending Schr"odinger-Bass to multi-step series for better joint drift and volatility modeling.

Findings

SBBTS accurately recovers stochastic volatility and correlation in the Heston model.

Synthetic data generated by SBBTS enhances forecasting accuracy and Sharpe ratio.

SBBTS outperforms prior methods in capturing key financial time series features.

Abstract

We study the problem of generating synthetic time series that reproduce both marginal distributions and temporal dynamics, a central challenge in financial machine learning. Existing approaches typically fail to jointly model drift and stochastic volatility, as diffusion-based methods fix the volatility while martingale transport models ignore drift. We introduce the Schr\"odinger-Bass Bridge for Time Series (SBBTS), a unified framework that extends the Schr\"odinger-Bass formulation to multi-step time series. The method constructs a diffusion process that jointly calibrates drift and volatility and admits a tractable decomposition into conditional transport problems, enabling efficient learning. Numerical experiments on the Heston model demonstrate that SBBTS accurately recovers stochastic volatility and correlation parameters that prior Schr\"odingerBridge methods fail to capture. Applied to S&P 500 data, SBBTS-generated synthetic time series consistently improve downstream forecasting performance when used for data augmentation, yielding higher classification accuracy and Sharpe ratio compared to real-data-only training. These results show that SBBTS provides a practical and effective framework for realistic time series generation and data augmentation in financial applications.